So, anyone using 256 bit hashes or higher (384 and 512) are overkill.
Also, some sites (like Just-Dice and CoinRoll) use the same seed on multiple rolls. So you need to raise your probability of cheating to the N'th power, where N is the number of rolls with the seed. The chance of breaking sha512 once is currently so close to zero as to be effectively zero. Raise that to the 200,000th power (or however many rolls you made with your current JD seed pair) and it just gets silly how tiny the difference between "provably" and "probably" gets.
To put it in perspective, Just-Dice is "probably" fair in the same way as a person sending Bitcoins "probably" owns the private key and didn't just guess it. Maybe he just got lucky and brute-forced the private key, but "probably" he didn't.
Thanks for the support. . . . .
Seriously though, I'm just using the words that should be used. It turns out that we still can't prove it, unfortunate as that may be. However it has to be better explained to people or they will call us marketing scams or something.
However, on this topic of using the same seed on multiple rolls, does this logic apply to the same seed (or the same group of seeds linked to each other) on cards games? For example, a 52 card deck that uses 52 different "card seeds" or "card secrets". If you reveal only the cards the player has, how "provable" or "probable" is it that all the other cards are rigged even if you can't see them?
If that question can be satisfied, then we have a partial solution to the poker issue (how to prove that mucked / discarded / folded cards are what they are, because only the original player knows them)... or I ask the other question "if the other player folded, does it matter that you don't know and can't prove what his cards are?"
psst, @dooglus, I made a thread specifically for poker, it's in the games sub-forum. Go there, I could use your input. Thanks.
Back to topic, what is a good level or high enough probability for us to consider as something provable? Certainly 2^16 is not enough, or 2^32 is still only 4 billion. Is 2^64 good enough? 2^80? 2^96? 2^112? Or do we "require" 2^128 at least?
My guess, is that we match what is considered "unbreakable" for the time being, which is 128 bit encryption as the minimum. Implementing something in Triple-DES at 112 bit, while not recommended is also "provably" unbreakable. DES was never cracked. It was simply brute-forced due to such a small key space.